Suppression of the rate of growth of dynamic heterogeneities and its relation to the local structure in a supercooled polydisperse liquid

Effect of Size Polydispersity on the Nature of Lennard-Jones Liquids

Polydisperse fluids are encountered everywhere in biological and industrial processes. These fluids naturally show a rich phenomenology exhibiting fractionation and shifts in critical point and freezing temperatures. We study here the effect of size polydispersity on the basic nature of Lennard-Jones (LJ) liquids, which represent most molecular liquids without hydrogen bonds, via two- and three-dimensional molecular dynamics computer simulations. A single-component liquid constituting spherical particles and interacting via the LJ potential is known to exhibit strong correlations between virial and potential energy equilibrium fluctuations at constant volume. This correlation significantly simplifies the physical description of the liquid, and these liquids are now known as Roskilde-simple (RS) liquids. We show that this simple nature of the single-component LJ liquid is preserved even for very high polydispersities (above 40% polydispersity for the studied uniform distribution). We also investigate isomorphs of moderately polydisperse LJ liquids. Isomorphs are curves in the phase diagram of RS liquids along which structure, dynamics, and some thermodynamic quantities are invariant in dimensionless units. We find that isomorphs are a good approximation even for polydisperse LJ liquids. The theory of isomorphs thus extends readily to size polydisperse fluids and can be used to improve even further the understanding of these intriguing systems.

Solid-liquid transition in polydisperse Lennard-Jones systems

We study melting of a face-centered crystalline solid consisting of polydisperse Lennard-Jones spheres with Gaussian polydispersity in size. The phase diagram reproduces the existence of a nearly temperature invariant terminal polydispersity (δ(t) =/~ 0.11), with no signature of reentrant melting. The absence of reentrant melting can be attributed to the influence of the attractive part of the potential upon melting. We find that at terminal polydispersity the fractional density change approaches zero, which seems to arise from vanishingly small compressibility of the disordered phase. At constant temperature and volume fraction the system undergoes a sharp transition from crystalline solid to the disordered amorphous or fluid state with increasing polydispersity. This has been quantified by second- and third-order rotational invariant bond orientational order, as well as by the average inherent structure energy. The translational order parameter also indicates a similar sharp structural change at δ =/~ 0.09 in case of T(*) = 1.0, φ = 0.58. The free energy calculation further supports the sharp nature of the transition. The third-order rotationally invariant bond order shows that with increasing polydispersity, the local cluster favors a more icosahedral arrangement and the system loses its local crystalline symmetry. Interestingly, the value of structure factor S(k) of the amorphous phase at δ =/~ 0.10 (just beyond the solid-liquid transition density at T(*) = 1) becomes 2.75, which is below the value of 2.85 required for freezing given by the empirical Hansen-Verlet rule of crystallization, well known in the theory of freezing.

Vibrational dynamics and boson peak in a supercooled polydisperse liquid

Vibrational density of states (VDOS) in a supercooled polydisperse liquid is computed by diagonalizing the Hessian matrix evaluated at the potential energy minima for systems with different values of polydispersity. An increase in polydispersity leads to an increase in the relative population of localized high-frequency modes. At low frequencies, the density of states shows an excess compared to the Debye squared-frequency law, which has been identified with the boson peak. The height of the boson peak increases with polydispersity and shows a rather narrow sensitivity to changes in temperature. While the modes comprising the boson peak appear to be largely delocalized, there is a sharp drop in the participation ratio of the modes that exist just below the boson peak indicative of the quasilocalized nature of the low-frequency vibrations. Study of the difference spectrum at two different polydispersity reveals that the increase in the height of boson peak is due to a population shift from modes with frequencies above the maximum in the VDOS to that below the maximum, indicating an increase in the fraction of the unstable modes in the system. The latter is further supported by the facilitation of the observed dynamics by polydispersity. Since the strength of the liquid increases with polydispersity, the present result provides an evidence that the intensity of boson peak correlates positively with the strength of the liquid, as observed earlier in many experimental systems.

Anisotropic spatially heterogeneous dynamics on the alpha and beta relaxation time scales studied via a four-point correlation function

We examine the anisotropy of a four-point correlation function G4(k[over ],r[over ];t) and its associated structure factor S4(k[over ],q[over ];t) calculated using Brownian dynamics computer simulations of a model glass forming system. These correlation functions measure the spatial correlations of the relaxation of different particles. We examine the time and temperature dependences of the anisotropy in both functions. We find that the anisotropy is strongest at nearest-neighbor distances at time scales corresponding to the peak of the non-Gaussian parameter alpha_{2}(t)=3deltar;{4}(t)/[5deltar;{2}(t);{2}]-1 but is still pronounced around the alpha relaxation time. We find that the structure factor S4(k[over ],q[over ];t) is anisotropic even for the lowest wave vector accessible in our simulation, suggesting that our system (and other systems commonly used in computer simulations) may be too small to extract the q[over ]-->0 limit of the structure factor. We find that the determination of a dynamic correlation length from S4(k[over ],q[over ];t) is influenced by the anisotropy. We extract an effective anisotropic dynamic correlation length from the small q behavior of S4(k[over ],q[over ];t) .